Exemplar Problems in Science for Class IX Exemplar Problems in Physics for Class XI Exemplar Problems in Chemistry for Class XI Exemplar Problems in Mathematics for Class XI Exemplar Problems in Biology for Class XI
EXERCISE 1.1
1. (C) 2. (C) 3. (D) 4. (D) 5. (D)
6. (C) 7. (D) 8. (C) 9. (C) 10. (C)
11. (B) 12. (A) 13. (D) 14. (B) 15. (B)
16. (C) 17. (C) 18. (B) 19. (A) 20. (A)
21. (C)
EXERCISE 1.2
1. Yes. Let x = 21, y = 2 be a rational number.
Now x + y = 21 + 2 = 21 + 1.4142 ... = 22.4142 ...
Which is non-terminating and non-recurring. Hence x + y is irrational.
2. No. 0 2✁0 which is not irrational .
3. (i) False. Although 2
3 is of the form p
q but here p, i.e., 2 is not an integer.
(ii) False. Between 2 and 3, there is no integer.
(iii) False, because between any two rational numbers we can find infinitely many rational numbers.
(iv) True. 2
3 is of the form p
q but p and q here are not integers.
(v) False, as ✂ ✄
42 2✁ 2 which is not a rational number.
(vi) False, because 12
4 2
3 which is a rational number.
(vii) False, because 15 5
5 1
3 which is p, i.e., 5 is not an integer.
4. (i) Rational, as 196 14
(ii) 3 18 9 2, which is the product of a rational and an irrational number and so an irrational number.
(iii) 9 1
27 3, which is the quotient of a rational and an irrational number and so an irrational number.
✁ ✂✁ , which is the quotient of a rational and an irrational.
(vi) 12 2
75 7, which is a rational number.
(vii) Rational, as decimal expansion is terminating.
(viii) ✄1✆ 5☎✝✄4✆ 5☎✞–3, which is a rational number.
(ix) Rational, as decimal expansion is non-terminating recurring.
(x) Irrational, as decimal expansion is non-terminating non-recurring.
EXERCISE 1.3 1. Rational numbers: (ii), (iii)
Irrational numbers: (i), (iv)
2. (i) –1.1, –1.2, –1.3 (ii) 0.101, 0.102, 0.103
3. (i) 2.1, 2.040040004 ... (ii) 0.03, 0.007000700007, ...
(iii) 5
12, 0.414114111 ... (iv) 0, 0.151151115 ...
(v) 0.151, 0.151551555 ... (vi) 1.5, 1.585585558 ...
(vii) 3, 3.101101110 ... (viii) 0.00011, .0001131331333 ...
(ix) 1, 1.909009000 ... (x) 6.3753, 6.375414114111 ...
7. (i) 1
ANSWERS 153
EXERCISE 1.4 1. 167
90 2. 1 3. 2.063 4. 7
5. 98 6. 1
2 7. 214
EXERCISE 2.1
1. (C) 2. (B) 3. (A) 4. (D) 5. (B)
6. (A) 7. (D) 8. (C) 9. (B) 10. (B)
11. (D) 12. (C) 13. (B) 14. (D) 15. (D)
16. (B) 17. (D) 18. (D) 19. (C) 20. (C)
21. (C)
EXERCISE 2.2 1. Polynomials: (i), (ii), (iv), (vii)
because the exponent of the variable after simplification in each of these is a whole number.
2. (i) False, because a binomial has exactly two terms.
(ii) False, x3 + x + 1 is a polynomial but not a binomial.
(iii) True, because a binomial is a polynomial whose degree is a whole number
✂ 1, so, degree can be 5 also.
(iv) False, because zero of a polynomial can be any real number.
(v) False, a polynomial can have any number of zeroes. It depends upon the degree of the polynomial.
(vi) False, x5 + 1 and – x5 + 2x + 3 are two polynomials of degree 5 but the degree of the sum of the two polynomials is 1.
EXERCISE 2.3
1. (i) One variable (ii) One variable
(iii) Three variable (iv) Two variables
2. (i) 1 (ii) 0 (iii) 5 (iv) 7
3. (i) 6 (ii) 1
5 (iii) –1 (iv) 1
5
4. (i) 1 (ii) 0 (iii) 3 (iv) –16
5. Constant Polynomial : (v) Linear Polynomials : (iii), (vi), (x) Quadratic Polynomials : (iv), (viii), (ix) Cubic Polynomials : (i), (ii), (vii)
6. (i) 10x (ii) x20 + 1 (iii) 2x2 – x – 1
7. 61, –143 8. 31
4 9. (i) –3, 3, – 39 (ii) – 4, –3, 0
10. (i) False (ii) True (iii) False (iv) True (v) True
11. (i) 4 (ii) 1 2 5. (i) 1092727 (ii) 10302 (iii) 998001
26. (i) (2x + 5)2 (ii) (3y – 11z)2 (iii) 1
ANSWERS 155
40. One possible answer is:
Length = 2a – 1, Breadth = 2a + 3
EXERCISE 2.4
1. –1 2. a = 5; 62 5. –120x2y – 250y3 6. x3– 8y3– z3– 6xyz
EXERCISE 3.1
1. (B) 2. (C) 3. (C) 4. (A) 5. (D)
6. (A) 7. (C) 8. (C) 9. (D) 10. (C)
11. (C) 12. (D) 13. (B) 14. (B) 15. (B)
16. (D) 17. (B) 18. (D) 19. (B) 20. (C)
21. (B) 22. (C) 23. (C) 24. (A)
EXERCISE 3.2
1. (i) False, because if ordinate of a point is zero, the point lies on the x-axis.
(ii) False (1, –1 ), lies in IV quadrant and (–1, 1) lies in II quadrant.
(iii) False, because in the coordinates of a point abscissa comes first and then the ordinate .
(iv) False, because a point on the y-axis is of the form (0, y).
(v) True, because in the II quadrant, signs of abscissa and ordinate are –, +, respectively.
EXERCISE 3.3
1. P(1, 1), Q(–3, 0), R(–3, –2), S(2,1), T(4, –2), O(0,0) 2. Trapezium
4. (i) Collinear (ii) Not collinear (iii) Collinear 5. (i) II (ii) III (iii) II (iv) I 6. (i) P(3, 2), R(3, 0), Q(3, –1) (ii) 0
7. II, IV, x-axis, I, III
8. C, D, E, G 10. (7, 0), (0, –7) 11. (i) (0, 0) (ii) (0,– 4) (iii) (5, 0) EXERCISE 3.4
1. C(–2, – 4) 2. (0, 0), (–5, 0), (0, –3) 3. (4, 3) 4. (i) A, L and O
(ii) G, I and O (iii) D and H 5. (i) (2, 1), (ii) (5, 7)
ANSWERS 157
2. False, since (0, 7) does not satisfy the equation.
3. True, since (–1, 1) and (–3, 3) satisfy the given equation and two points determine a unique line.
4. True, since this graph is a line parallel to y-axis at a distance 3 units (to the right) from it.
5. False, since the point (3, – 5) does not satisfy the given equation.
6. False, since every point on the graph of the equation represents a solution.
7. False, since the graph of a linear equation in two variables is always a line.
EXERCISE 4.3 1. Graph of each equation is a line passing through (0, 0).
2. (2, 3)
3. Any line parallel to x-axis and at a distance of 3 units below it is given by y = –3
4. x + y = 10 5. y = 3x 6. 5 3 7. (i) one (ii) Infinitely many solutions 8. (i) (4, 0) (ii) (0, 2)
4. (i) 30°C (ii) 95°F (iii) 32°F,
6. y = mx, where y denotes the force, x denotes the acceleration and m denotes the constant mass. 1. False, it is valid only for the figures in the plane.
2. False, boundaries of the solids are surfaces.
3. False, the edges of surfaces are line.
4. True, one of the Euclid’s axioms.
5. True, because of one of Euclid’s axioms.
6. False, statements that are proved are theorms.
7. True, it is an equivalent version of Euclid’s fifth postulate.
8. True, it is an equivalent version of Euclid’s fifth postulate.
9. True, these geometries are different from Euclidean geometry.
EXERCISE 5.4
1. Answer this question on the same manner as given in the solution of Sample Question 1 in (E).
3. No 4. No 5. Consistent
ANSWERS 159
EXERCISE 6.1
1. (C) 2. (D) 3. (A) 4. (A) 5. (D)
6. (A) 7. (C) 8. (B)
EXERCISE 6.2
1. x + y must be equal to 180°. For ABC to be a line, the sum of the two adjacent angles must be 180°.
2. No, angle sum will be less than 180°.
3. No, angle sum cannot be more than 180°.
4. None, angle sum cannot be 181°.
5. Infinitely many triangles. sum of the angles of every triangle is 180°.
6. 136°.
7. No, each of these will be a right angle only when they form a linear pair.
8. Each will be a right angle. Linear pair axiom .
9. l || m because 132° + 48° = 180°, p is not parallel to q, because 73° + 106° 180°.
10. No, they are parallel
EXERCISE 6.3 7. 90° 8. 40°, 60, 80°
EXERCISE 7.1
1. (C) 2. (B) 3. (B) 4. (C) 5. (A)
6. (B) 7. (B) 8. (D) 9. (B) 10. (A)
11. (B)
EXERCISE 7.2 1. QR; They will be congruent by ASA.
2. RP; They will be congruent by AAS.
3. No; Angles must be included angles.
4. No; Sides must be corresponding sides.
5. No; Sum of the two sides = the third side.
6. No; BC = PQ.
7. Yes; They are corresponding sides.
8. PR; Side opposite the greater angle is longer.
9. Yes; AB + BD > AD and AC + CD > AD.
10. Yes; AB + BM > AM and AC + CM > AM.
11. No; Sum of two sides is less than the third side.
12. Yes, because in each case the sum of two sides is greater than the third side.
EXERCISE 7.4 1. 60°, 60°, 60°
3. It is defective to use ✄ABD = ✄ACD for proving this result.
19.✄B will be greater.
EXERCISE 8.1
1. (D) 2. (B) 3. (C) 4. (C) 5. (D)
6. (C) 7. (D) 8. (C) 9. (B) 10. (D)
11. (C) 12. (C) 13. (C) 14. (C)
EXERCISE 8.2
1. 6 cm, 4 cm; Diagonals of a parallelogram bisect each other.
2. No; Diagonals of a parallelogram bisect each other.
3. No; Angle sum must be 360°.
4. Trapezium.
5. Rectangle.
6. No; Diagonals of a rectangle need not be perpendicular.
7. No; sum of the angles of a quadrilateral is 360°.
8. 3.5 cm, as DE =1 2AC.
9. Yes; because BD = EF and CD = EF.
10. 55°, ✄F = ✄A and ✄A = ✄C.
11. No; Angle sum of a quadrilateral is 360°.
ANSWERS 161
12. Yes, Angle sum of a quadrilateral is 360°.
13.✶ ✁✂ 14. ❝✄